Question

if alpha and beta are the quadratic polynomial f of x is equal to X square + X - 2 then find the value of one by Alpha minus one by beta​

Answer 1

f(x) = x² + x - 2

1/α - 1/β = (β - α)/αβ

α + β = -(Coefficient of x)/Coefficient of x²

=> α + β = -1

αβ = Constant/Coefficient of x²

=> αβ = -2

(α + β)² = α² + 2αβ + β²

=> (-1)² = α² + 2(-2) + β²

=> 1 = α² - 4 + β²

=> α² + β² = 5

(α - β)² = α² + β² - 2αβ

=> (α - β)² = 5 - 2(-2)

=> (α - β)² = 9

=> α - β = 3

β - α = (-1)(α - β)

β - α = (-1)(3) = (-3)

Substituting, we get

(-3)/(-2)

or

3/2